## A Generalized Klein Gordon Equation with a Closed System Condition for the Dirac-Current Probability Tensor

**Authors:** E. P. J. de Haas

By taking spin away from particles and putting it in the metric, thus following Dirac's vision, I start my attempt to formulate an alternative math-phys language, biquaternion based and incorporating Clifford algebra. At the Pauli level of two by two matrix representation of biquaternion space, a dual base is applied, a space-time and a spin-norm base. The chosen space-time base comprises what Synge called the minquats and in the same spirit I call their spin-norm dual the pauliquats. Relativistic mechanics, electrodynamics and quantum mechanics are analyzed using this approach, with a generalized Poynting theorem as the most interesting result. Then moving onward to the Dirac level, the M{\"o}bius doubling of the minquat/pauliquat basis allows me to formulate a generalization of the Dirac current into a Dirac probability/field tensor with connected closed system condition. This closed system condition includes the Dirac current continuity equation as its time-like part. A generalized Klein Gordon equation that includes this Dirac current probability tensor is formulated and analyzed. The usual Dirac current based Lagrangians of relativistic quantum mechanics are generalized using this Dirac probability/field tensor. The Lorentz transformation properties the generalized equation and Lagrangian is analyzed.

**Comments:** 42 Pages. Improved Lorentz transformation of the Dirac spinors.

**Download:** **PDF**

### Submission history

[v1] 2018-10-21 15:35:40

[v2] 2018-10-23 06:00:17

**Unique-IP document downloads:** 16 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*